Wait for it to burn down so there are plenty of white coals. You don't want lots of "fire". Fire is pretty to look at, but more unpredictable to cook in then hot white coals.

While the fire is burning down, wash and prep your potatoes to bake as you would normally.

Wrap them tightly in tin foil.

Once the fire is burned down to hot, white coals, toss the potatoes directly onto the coals.

Wait until cooked (roughly 40 minutes for an average sized potato, on an average fire, adjust accordingly).

If you have a shovel or something, put some coals on to the actual potato as well, so you're completely surrounding it. It'll speed it up. If you don't have anything handy to handle coals, make sure you flip them half way.

Remove carefully and enjoy.

The moisture of a potato, will allow it to cook without burning. Just make sure you wrap them with no exposed areas, in order to trap the steam.

If not eating immediately, do not leave potatoes in foil wrapping. Unwrap and let surface dry. This is more of a concern when potatoes not washed well before cooking, or not fully cooked. see cooking.stackexchange.com/questions/15339/…
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TFDSep 20 '11 at 22:59

You can use a shovel to get some coal out of an active fire as well, and not wait for it to die all the way...I was the cook for an adventure trip down a river for several summer and there are times when you want cooking coals but still need your fire going.
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rfuscaSep 20 '11 at 23:07

We got more consistent results if we turned them once.
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dmckeeSep 21 '11 at 13:23

My family used to make these when car camping, it was fairly easy. We'd usually make the potatoes after the first day, this gave the advantage of controlling the heat of the earth somewhat due to the 1 day of camping prior to using the fire to bake stuff.

The main requisite is a mature fire, with lots of ash in a fairly thick layer and good coaling.

If using foil, we would coat the potatoes with oil or butter, thinly, wrap with foil tightly, and place in an area where coals were covered thickly with hot ash, then rake more ash over the top of the potatoes and cover that with coals. As the cooking progressed, the top coals would be renewed as needed, and all noses were on the lookout [err smellout?] for burned potato. For burning, potatoes were removed to a cooler spot, out of the coals, using only the radiant heat of the fire to finish cooking.

For potatoes au natural, the same procedure was followed, making sure the was no direct coal to potato contact. The results are mostly the same, the uncovered potatoes come out a bit dryer and the skin is not edible.

We would always cook lots and save the leftovers to make fried potatoes in the morning.

Another thing we would do, [this has nothing to do with your question, but is cool] especially when backpacking, was to take small plastic bags and put 1/2 cup/125 ml of Bisquick or some other self rising batter mix, a small box of raisins, and a square of foil, buttered on one side and folded up. At camp, we would take out the raisin box and foil, add water to the bag with the batter mix, squish it around until mixed, add in the raisins, squeeze the (thick) batter into the center of the foil, fold up the foil around the batter (leaving room for expansion) and bake the raisin muffin on the fire surround, using radiant heat to bake it.

There are special purpose stove-top waterless clay potato cookers (or bakers), often referred to as a Kartoffel Teufel (potato devil). The preparation is extremely simple - just place the potatoes in the pot (without water) and on the stove and cook until tender. The taste is very similar to campfire.